Reduce to lowest terms: $ \dfrac{6}{7} \div \dfrac{1}{6} = {?}$
Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{1}{6}$ is $ \dfrac{6}{1}$ Therefore: $ \dfrac{6}{7} \div \dfrac{1}{6} = \dfrac{6}{7} \times \dfrac{6}{1} $ $ \phantom{ \dfrac{6}{7} \times \dfrac{6}{1}} = \dfrac{6 \times 6}{7 \times 1} $ $ \phantom{ \dfrac{6}{7} \times \dfrac{6}{1}} = \dfrac{36}{7} $